Question: Solve for $x$ and $y$ using substitution. ${x+2y = 4}$ ${x = -5y+7}$
Solution: Since $x$ has already been solved for, substitute $-5y+7$ for $x$ in the first equation. ${(-5y+7)}{+ 2y = 4}$ Simplify and solve for $y$ $-5y+7 + 2y = 4$ $-3y+7 = 4$ $-3y+7{-7} = 4{-7}$ $-3y = -3$ $\dfrac{-3y}{{-3}} = \dfrac{-3}{{-3}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = -5y+7}\thinspace$ to find $x$ ${x = -5}{(1)}{ + 7}$ $x = -5 + 7$ ${x = 2}$ You can also plug ${y = 1}$ into $\thinspace {x+2y = 4}\thinspace$ and get the same answer for $x$ : ${x + 2}{(1)}{= 4}$ ${x = 2}$